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A wheel, originally rotating at 126 rad/s undergoes a constant angular deceleration of 5.00 rad/s2. What is its angular
A wheel, originally rotating at 126 rad/s undergoes a constant angular deceleration of 5.00 rad/s2. What is its angular speed after it has turned through an angle of 628 radians?
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The equation for angular motion is ωf^2 = ωi^2 + 2αΔθ, where ωf is the final angular speed, ωi is the initial angular speed, α is the angular acceleration (negative for deceleration), and Δθ is the change in angle.
Rearranging the equation for ωf gives ωf = sqrt(ωi^2 + 2αΔθ).
Substituting the given values gives ωf = sqrt((126 rad/s)^2 + 2*(-5.00 rad/s^2)*628 rad) = sqrt(15876 rad^2/s^2 - 6280 rad^2/s^2) = sqrt(9596 rad^2/s^2) = 98 rad/s.
So, the wheel's angular speed after it has turned through an angle of 628 radians is 98 rad/s.
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